New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type. (English) Zbl 1450.45002
Algebraic sums of Wiener-Hopf and Hankel operators have received attention in the last years, cf. [L. P. Castro et al., Math. Nachr. 269–270, 73–85 (2004; Zbl 1082.47024); N. Karapetiants and S. Samko, Equations with involutive operators. Boston, MA: Birkhäuser (2001; Zbl 0990.47011)], relevant motivations being the applications to wave diffraction phenomena. In the present paper the authors introduce some mathematical tools suitable for the study of the corresponding equations. Namely, convolutions exhibiting factorization properties are considered, and precise solvability properties are deduced for the equations. An explicit formula for the solution is presented and a Shannon sampling formula is also obtained in this context.
Reviewer: Luigi Rodino (Torino)
MSC:
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 44A35 | Convolution as an integral transform |
| 42A85 | Convolution, factorization for one variable harmonic analysis |
| 43A32 | Other transforms and operators of Fourier type |
| 45P05 | Integral operators |
Keywords:
convolution; factorization; Fourier integral operator; Hankel operator; integral equation; Wiener-Hopf operatorReferences:
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